pascal's triangle

While reading SICP recently, I came across a exercise which asks reader to generate Pascal's Triangle using recursion.

There are many interesting observations about values that get generated in this triangle. One thing I noticed is, sum all the values generated at each level = 2^(level-1) if you start counting levels from 1.

So I thought, lets give it a try .. and it was not difficult to come up with this version.

# Pascal's triangle

# store to avoid recomputation of the same values
$val_store = {}

def getval(row, position)
    val = 0
    if position <= 0 or row <= 0 or position > row
        val = 0
    end
    if position == 1 or row == 1 or row == position
        val = 1
    else
        # first check in the store
        if $val_store["#{row}:#{position}"]
            val = $val_store["#{row}:#{position}"]
        else
            val = getval(row - 1, position - 1) + getval(row - 1 , position)
            $val_store["#{row}:#{position}"] = val
        end
    end
    return val
end

def get_row_vals(row)
    row_vals = []
    i = 0
    row.times {
        i = i + 1
        row_vals << getval(row, i)
    }
    return row_vals
end

rows = ARGV[0].to_i || 20
i = 1
rows.times {
    sum = 0

    row_vals = get_row_vals i
    row_vals.each { |val|
        sum += val
    }
    puts "Sum: #{sum} Row #{i}: #{row_vals.inspect}"
    i = i + 1
}
puts "Store size: #{$val_store.length}"

Next thing ... try to implement using lisp?